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Stephen Williams: „Quasi-equilibrium and the Emergence of Solid Behaviour in Amorphous Materials”
Research School of Chemistry, The Australian National University, Canberra, Australia

When a system is very slow to relax it may become trapped in a particular region of microscopic phase space. Under these conditions, two examples of a given material may appear macroscopically equivalent, despite being microscopically distinct. Such a system may relax to a state of quasi-equilibrium. An important example is the amorphous solid state.

A fluid cannot support a stress. If we subject a fluid to a sudden change in strain, a nonequilibrium stress results that then relaxes to zero. This relaxation cannot be understood in terms of equilibrium statistical mechanics. In contrast if we subject a solid to the same protocol, initially a nonequilibrium stress results, which then relaxes to some perturbed equilibrium or quasiequilibrium non-zero stress. Even if the solid like material is able to flow on some much longer time scale, we can still accurately quantify the observed non-zero stress (on some time scale) using equilibrium or quasi-equilibrium statistical mechanics. We take this to be the fundamental difference between a solid and a fluid.

Recently we have developed quasi-equilibrium statistical mechanics for the case of planar shear. This work shows how solid behaviour emerges in amorphous materials from microscopic considerations. Here the relevant quasi-equilibrium statistical mechanics will be reviewed. It will be shown how the response in the stress, to a change in the strain, is qualitatively different for a quasiequilibrium solid, relative to a supercooled fluid. New molecular dynamics computer simulation results will be presented. These show convincingly how this qualitative change emerges very sharply, upon crossing from a supercooled fluid to a history dependent quasi-equilibrium solid (i.e. a glass).